Throughout this paper we use Galactocentric cylindrical coordinates \((R,\,\phi ,\,Z)\)  with \(R\)  pointing outwards from the Galactic center (GC), the azimuthal \(\phi \)  in the direction of Galactic rotation, and \(Z\)  positive towards the north Galactic pole. The Galactocentric distance of the Sun is fixed at \(R_0=8.122\,\mathrm {kpc}\)  [1]}, and the vertical offset of the Sun from the Galactic mid-plane is assumed to be \(Z_\odot =20.8\)  pc [2]}. The sample is located within \(5<R<15\,\mathrm {kpc}\)  and \(|Z|<3\,\mathrm {kpc}\) . Since the reference of the Galactocentric system is fixed at the GC, we need to know the velocity of the Sun. The azimuthal component of the solar velocity (\(v_\odot \) ) can be obtained directly from the proper motion of Sgr A* along the Galactic longitude, i.e., \(\mu _{\rm {Sgr A*}}=-6.411\,\mathrm {mas\,yr}^{-1}\)  [3]}, which yields \(v_\odot =246.8\,\mathrm {km\,s}^{-1}\) . The radial and vertical velocities of the Sun are taken from the widely used \(U_\odot =11.1\,\mathrm {km\,s}^{-1}\)  and \(W_\odot =7.25\,\mathrm {km\,s}^{-1}\)  given by [4]}. In our sample, the velocity is confined to \(|V_R|<200\,\mathrm {km\,s}^{-1}\) , \(-80<V_\phi <320\,\mathrm {km\,s}^{-1}\)  and \(|V_Z|<150\,\mathrm {km\,s}^{-1}\)  by using the \(3\sigma \)  criterion to avoid outlier velocities. Finally, a total number of \(N=488209\)  K giants remain.
